And now, for the second part about #TwinPrimeConjecture, as a layman, I managed to understand the whole proof but without the full rigor of formal proofs (everything is explained in layman terms before and after equations) because I didn't remember how to reach the probabilistic equation[1] and some equation transformations become too hard for me.
But this didn't worsen my reading experience [2]. Nonetheless my reading & understanding got a bit slower because the second part require a bit more of memory to interconnect the pieces.

Fun story: I got stuck a long time at page 6 trying to grasp/integrate how to use the definition of primes of Type-A,B,C. Only to finally understand I was being too myopic by searching the meaning of the definition in self-contained Type-A or B or C, instead of conceptualizing ‘k’ as the same current dial for both Type-A Type-B and Type-C. This was very self-evident but my brain can be dumb. And so then, to my surprise, the next page had that explanation, so even for a buggy-brain it would have been explained and I could have avoided this time-sink if only I've read the next page ...

All in all, a very good experience leaving memorable insights that exposed a fresh and useful way of thinking and perceiving things, that I'm sure, will be useful in other contexts, and bring joy and a feeling of unbound space-like possibilities just thinking about.

3/3

The first part, about the #PrimeClockMethod is my favorite part and also the simplest one. This part feels like reading an introduction giving us a uncanny paranoiac feeling of doom about the hard thinking to come. Except that contrary to what our instinct is screaming to us, it never come, and the ease of reading and comprehension is maintained trough the paper while still achieving to give us wonderful insight.

The structure is a well crafted continuous narrative (can be read linearly) that alternate between showing us a good idea/point_of_view, and then exposing us the next piece of problem so straight forwardly that we can try to solve it like if it was a puzzle. Making us feel smart because we manage to find the solution that is just afterwards explained/confirmed.
(a case of "defining the problem the right way is the biggest part of the problem", but then, the reader is allowed the joy of doing the final symbolic act, akin to parents doing everything but nonetheless letting the child do the final act autonomously and without hints because the final thing to do is already setup to be self-evident but this doesn't remove the joy and feeling of accomplish of doing so xD)

That first part is only 3 pages long, so even if you don't wanna read the second part about the #TwinPrimeConjecture, I encourage you to read those few pages. It will leave you a long and profound impression effortlessly, I can tell you, I'm still thinking about it 1 month after reading it, and I only read it once.
( and by saying this, my vice of being paralyzed unable to reviewing this paper for almost 1 month can finally become a virtue of a justified laps of time to prove that it has left me a long lasting impact)

2/3